Non-line of sight wireless communication system and method

ABSTRACT

A non-line of sight backhaul system and method are described that provides self-alignment of the antennas beams of the wireless radios of the system, that provides robust operation in licensed and unlicensed frequency bands, that facilitates the use of a reduced number of frequency channels from M to 1 and that enables operation in a non-line of sight (NLOS) propagation environment.

PRIORITY CLAIMS/RELATED APPLICATIONS

This application claims priority under 35 U.S.C. § 120 and is acontinuation of U.S. patent application Ser. No. 15/012,615 filed onFeb. 1, 2016 and entitled “Non-Line of Sight Wireless CommunicationSystem and Method”, (now U.S. Pat. No. 10,432,275, issued on Oct. 1,2019) which claims priority under 35 U.S.C. § 120 and is a continuationof U.S. patent application Ser. No. 13/445,863, filed on Apr. 12, 2012and entitled “Non-Line of Sight Wireless Communication System andMethod”, now U.S. Pat. No. 9,252,908 issued on Feb. 2, 2016), U.S.patent application Ser. No. 13/445,869, filed on Apr. 12, 2012 andentitled “Non-Line of Sight Wireless Communication System and Method”(now U.S. Pat. No. 9,456,354 issued on Sep. 27, 2016) and U.S. patentapplication Ser. No. 13/445,861, filed on Apr. 12, 2012 and entitled“Non-Line of Sight Wireless Communication System and Method” (now U.S.Pat. No. 9,325,409 issued on Apr. 26, 2016), all of which areincorporated herein by reference.

FIELD

The disclosure relates a wireless backhaul system that uses non-line ofsight wireless communications and the non-line of sight wirelesscommunications system and method.

BACKGROUND

A backhaul system is a communication system that is used to communicatecertain data from a cellular network, for example, back to the centralsystem in a communications system. Various different backhaul systemsare well known that are both wireless communication systems and wiredcommunication systems. Most of the current wireless backhaul systems arepoint to point (P2P) systems that operate in the licensed FDD (frequencydivision multiplexed or a frequency division protocol) microwave bandsfrom 6 GHz to 80 GHz. These systems use high gain parabolic dishes whichmust be manually pointed and also rely on the low sidelobe performanceof the dish to reduce (but not eliminate) co-channel interference.Moreover, these products must be used where line-of-sight is available.

These existing backhaul systems do not provide self alignment andrealignment of the antenna beams or any increase in effective linkspectral efficiency by using interference cancellation. These existingsystems also do not operate in a non-line-of sight propagationenvironment, are not able to double the spectral efficiency by using twopolarizations in this environment and have reduced link reliability dueto fading. These existing systems do not cancel radio interference tooptimize signal to interference and noise ratio (SINR) and do not cancelinterference from other self-generated co-channel interference. Theseexisting systems also do not have multi-target beam-forming thatenhances spectral efficiency and can provide exceptional dataconcentration in small amounts of spectrum.

Furthermore, given the shortage of spectrum for broadband wireless andthe need to increase both link rate and network capacity, wirelesscarriers are migrating from a traditional macro-cellular networktopology 10 to a micro-cellular and pico-cellular topologies 20 as shownin FIG. 1 . That is, instead of using a few high-high poweredbase-stations to cover large areas, they supplement these with manyoutdoor micro-cells and pico-cells as shown in FIG. 1 .

The base station capacity (measured in Mbps) has been increasing slowlyas operators migrate from 2.5G and 3G technologies (HSDPA, HSPA, CDMA2000, CDMA EVO, etc) to 4G technologies (WiMax and LTE). However, 4Gtechnology increases spectral efficiency only 50% relative to theprevious generation. Yet, 4G will not solve the 10-fold increase neededto maintain a macro-cell topology while increasing user capacity. Hence,emerging wireless architectures solve the throughput problem byincreasing “capacity density” (measured in Mbps per km²), and not byincreasing capacity alone.

Increasing capacity density 10-fold can be solved by a dense deploymentof micro- and pico-cells. Although these cells have limited range (100to 500 meters), they retain the capacity similar to macro-cells, for theLTE standard 15 Mbps in 10 MHz of bandwidth and 39 Mbps in 10 MHz ofbandwidth with 3-sectored implementations. Thus, a macro-cell with arange of 1 km (urban propagation) and capacity density of 15 Mbps/km²,evolves into a micro-cellular topology featuring a capacity density of135 Mbps/km² using 9 micro-cells.

Thus, it is desirable to provide a non-line of sight backhaul system andmethod that overcomes the above limitations of existing backhaul systemsand it is to this end that the disclosure is directed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a typical backhaul system migration from macro-cells;

FIG. 2 illustrates an example of a non-line of sight system such as anon-line of sight, point to multipoint backhaul star architecturesystem;

FIG. 3 illustrates an example of an implementation of a wirelessnon-line of sight backhaul system;

FIG. 4 illustrates details of the operation of the wireless non-line ofsight backhaul system;

FIG. 5 illustrates a method for multiplicative spectral efficiency inthe non-line of sight system;

FIG. 6 illustrates an example of an implementation of both concentratingbackhaul radio and the terminating backhaul radios of the system;

FIG. 7 illustrates an example of a 2-dimensional beamforming networksubsystem;

FIG. 8 illustrates an implementation of the communication protocolbetween the CBR and TBR of the system;

FIG. 9 illustrates a set of uplink and downlink RF channels on thesystem; and

FIG. 10 illustrates the RD channels.

DETAILED DESCRIPTION OF ONE OR MORE EMBODIMENTS

The disclosure is particularly applicable to a wireless non-line ofsight backhaul system and method described below and it is in thiscontext that the disclosure will be described. It will be appreciated,however, that the system and method has greater utility since thewireless non-line of sight backhaul system and method can be implementedin other manners that are within the scope of the disclosure.

The system is a wireless, non-line of sight backhaul system that enablesself alignment and realignment of the antennas beams of the wirelessradios of the system, that provides robust operation in licensed andunlicensed frequency bands, that facilitates the use of a reduced numberof frequency channels from M to 1 and that enables operation in anon-line of sight (NLOS) propagation environment. The system may providean increase in effective link spectral efficiency by using ExtremeInterference Cancellation (EIC) and up to double the spectral efficiencyby using two polarizations. The system also provides an improvement inlink reliability by reducing fading. The system also cancels the radiointerference to optimize signal to interference and noise ratio (SINR)and cancels interference from other self-generated co-channelinterference. The system can be operated in a line of sight, near lineof sight and non-line of sight radio frequency (RF) propagationenvironments. The system also provides multi-target beam-forming thatenhances spectral efficiency and can provided exceptional dataconcentration in small amounts of spectrum. The non-line of sight systemdescribed below may be use a single radio frequency channel to supportthe wireless backhaul requirements of a carrier. Now, an implementationof the system is described in more detail.

FIG. 2 illustrates an example of a non-line of sight system 30 such as anon-line of sight, point to multipoint backhaul star architecturesystem. In one implementation, the non-line of sight system has a startopology with a point-to-concentrating multipoint (P2CMP) connectivitythat has two types of wireless nodes: concentrator backhaul radios(CBRs) and terminating backhaul radios (TBRs). The non-line of sightsystem 30 may also have a point to point architecture, a multiple pointto point architecture and a point to multipoint architecture. Each nodein this wireless architecture may be referenced simply as concentratornodes (CN) and end nodes (EN) evocative of their positions in thenetwork. Each concentrator node aggregates traffic from L full bandwidthTBRs with capacity Q for a total of L*Q bps. Note that the P2CMP alsoembodies the notion of L*L_(sb) TBRs links with capacity Q/L_(sb)connected to the CBR where L_(sb) is the number of subbands using eitherfrequency division multiplexing (FDM) or time division multiplexing(TDM). Each TBR is attached to the micro or pico base station thusproviding wireless backhaul connectivity. The physical connection withthe TBR is via the native output of the base station.

FIG. 3 illustrates an example of an implementation of a wirelessnon-line of sight backhaul system 50. The system has one or more links(microwave or RF links) terminated at a central backhaul radio 54 (CBR).In one example, the system has M links where M is a number greaterthan 1. Each link is comprised of a termination backhaul radio 52 (TBR)and 1/Mth of the CBR with a data capacity of Q bps per link where Q is apredetermined number that ranges from 1 to 15 bps. The data capacitymeasured at the CBR 54 is M*Q bps. Each link is comprised of a sharedadaptive array 58 at the CBR 54 and one or more directional antennas 60at each TBR. Optionally, the antenna at each TBR can be realized with anadaptive array. If each TBR has an adaptive array, then the TBR willself align its antenna pattern to the CBR. This is accomplished bycomputing the array's beamforming weights using the frame start preamble(FSP) of the CBR as a reference. The weights may be computed from theWeiner equation using the array covariance matrix and thecross-correlation of the data with the FSP. Alternately, known referencesymbols in the CBR may be used instead of the FSP as the desired signal.For all TBR antenna types, the CBR will self align its antenna patternto all of the TBRs. When adaptive arrays are used for both the CBR andTBRs, the CBR and TBR adaptive arrays seek to maximize thesignal-to-interference and noise ratio (SINR) by pointing an antennabeam toward the other end of the link, and by reducing interference bydirecting spatial nulls of the array toward these sources of linkdegradation.

In more detail, the wireless backhaul system 50 may have an architectureas shown in FIG. 3 which there is a central/concentrating backhaul radio(CBR) 54 that is communicating with up to 10 terminating backhaul radios(TBRs) 52 and each of the TBRs may be located adjacent a picocell andprovide a connection between the picocell and the network as a backhaulnetwork. In more detail, a wireless backhaul is used to connect wirelessbase stations to the core network and/or the operator'spoint-of-presence and facilitates the backhaul connection of all typesof base stations, including femto, pico, micro, mini, and macro basestations. Moreover, this same technology is effective in wirelessbroadband bridging and last mile extensions of copper, cable and fiberplant. The wireless backhaul system described herein is able to handlethe capacity requirements of 3G systems, 4G systems and future wirelessprotocols (including wireless data protocols.)

The CBR 54 may further comprise an adaptive antenna array 58 (thatpermit multiple simultaneous beams of the same channel) and a piece ofCBR shared equipment 56. The CBR 54 can handle multiple simultaneousbeams using the same channel because the system is able to performextreme interference cancellation to eliminate interference between thevarious TBR signals. In this invention, this is accomplished bydirecting spatial nulls in the array antenna pattern in the directionsof all interfering TBR while forming a beam peak in the direction of thedesired TBR. Moreover, this process is replicated for each desired TBRconnected to the CBR thus forming multiple beams and mutual spatialnulling that cancels interference. In conventional PtMP systems, theCBR-like hub can usually handle multiple beams, but those beams each useseparate RF channels which wastes bandwidth.

While the maximum SINR optimization criterion is described above, othercriteria also may be used (e.g. max SIR beamforming or non-linear datadirection beamforming). Of particular importance is an extremeinterference cancellation (EIC) feature at each TBR 52 if a high order(6 to 256 elements) adaptive array is employed at the TBR 52 using theequations (E1) through (E23) and equation G1 described below. Thisfeature enables a boost in the SINR from 10 dB to 25 dB nominally intypical system deployments. In addition, depending on the coding rate,EIC is projected to boost link capacity from 1-2 bps/Hz to over 5-6bps/Hz. Furthermore, if dual polarizations are used, then the capacitycan be increased by a factor of 2 (maximum).

Multi-target beamforming introduces a unique beam and interferencenulling solution for each TBR 52. Thus, the CBR 54 issues M beams, oneeach to M TBRs. Each of these beams may use one of M separate frequencychannels, or one of M separate subchannels within the overall channel.Alternately, the beams may use the same frequency channel. In the casein which the beams use the same frequency channel, the adaptive arrayeliminates the interference from the M−1 other beams using spatialnulling techniques. Alternately, the beams may use a combination of M/Kchannels or subchannels where K is integer sub-multiple of M. In thiscase, the adaptive array eliminates the interference from the M/K−1other beams using spatial nulling techniques.

The non-line-of-sight backhaul operation involves angle and delay spreadarray processing to remove the effects of frequency selective channelresponses due to multipath. This process is described using the channelmodel described in Equation (B1) through (B2) Moreover, it deals withmultiple copies of the signal arriving from Q disparate angles ofarrival. Conceptually, this involves creating a separatebeamforming/null steering solution for each of Q signal paths at eachdelay spread value, then adaptive combining the Q outputs of theindividual paths to optimize the SINR of the link. Two-dimensionalbeamforming in space for each time-delayed multipath is used. This maybe implemented as a tapped delay line beamformer. Alternately, thebeamforming operations may be realized efficiently by transforming thearray signals between the frequency and time domains.

For the case of dual polarization, the 2 dimensional beamformer canoperate on 2M antennas where M in the number of antennas with onepolarization. Many algorithms as described above yield an optimalsolution to this problem if all antennas/polarizations are used in theformulation.

FIG. 4 illustrates details of the operation of the wireless non-line ofsight backhaul system. As shown, a NLOS signal path (that may bediffracted or reflected) is used. Each TBR 52, using its adaptiveantenna array (to receive multiple signals) and a beamformer (BFN), canperform spatial and temporal equalization of the various signalsreceived by the antenna array (A₁, . . . , An) to extract the signalfrom the multipath signals caused by the NLOS signal paths. This allowsthe wireless backhaul system to work without line of sight between theradios.

Beamforming and Interference Cancellation

Adaptive beamforming is used at both the CBR 54 and TBRs 52 to increasearray gain and reduce interference. In adaptive beamforming, N₁ and N₂antennas, respectively, are adaptively combined to yield the optimumsignal-to-interference and noise (SINR) ratio at both ends of the link.Physically, a CBR adaptive beam is pointed in the direction of the TBRand the TBR points its adaptive beam back to the CBR as shown in FIG. 3. Moreover, N₁-1 spatial nulls (zeros) are directed at interferencecaused by other TBRs (managed interference) in the network while N₂-1spatial nulls (zeros) are directed at interference caused by other CBRs.In practical systems, the number of antennas N₁ and N₂ can range from 2to 256. By cancelling all interference, the desired link may achieve itshighest capacity since it will be essentially noise limited rather thatinterference limited. Moreover, since a range of a link is now notinterference limited but is dependent only on path loss to the TBR'slocation, the EIRP and the receiver's sensitivity are enhanced by the2-dimensional beamforming gain at the TBR and CBR.

Automatic Beamsteering, in Changing Multipath Propagation and SINROptimization

No special knowledge of the TBR's direction of arrival, location, or theinterferers' directions of arrival is required to automatically pointthe optimized antenna beams between the TBR and CBR. Moreover, theadaptive beamforming solution optimizes the receiver SINR and may beupdated rapidly to follow any temporal changes in the signal's angle ofarrival, power levels, phase, time delay or other changes in the vectorsignature received on the array due to multipath or time-varyingmultipath. Special reference symbols embedded within the uplink anddownlink transmission provide the signal structure so that algorithmscan generate adaptive weights which cancel interference and direct beamseven in time varying propagation channels without operator intervention.For example, those processes are described in Equations (C1) through(C23) for Space Time Adaptive Processing (STAP) and Equations (E1)through (E15d) through Space Frequency Adaptive Processing (SFAP).

Multi-Beam and Multiplicative Spectral Efficiency

FIG. 5 illustrates a method for multiplicative spectral efficiency inthe non-line of sight system. In the system, Multi-beam array processingextends single beam beamforming by providing L simultaneous links to LTBRs 52 within the footprint of the CBR 54 using the same RF channel atfull bandwidth. It accomplishes this by using at least N−1 spatial nullsper link to remove co-channel interference caused by other L−1 TBRs inattached to the CBR cell as shown in FIG. 5 . In the system, each linkoptimizes SINR in the presence of the co-channel self-interference tomaximize throughput.

If the system uses time-division duplexing (TDD or time divisionduplexing), the system described here will preserve the “nulldirections” in the downlink transmission by using a retro-directivecomputation of the array processing solution. As a result, TBRsexperience no undesired interference from the other in-cell links andother out-of-cell CBRs. Thus, the downlink capacity is maximized for allin-cell links and out-of-cell CBRs.

Universal Frequency Reuse

TDD multi-beam array processing described above and used by the systemhas remarkable implications. For example, the capacity of the CBR hasincreased L-fold because the CBR now serves L times as many TBRs in anytime epoch. Furthermore, the spectral efficiency is L times greater.This enables broadband backhaul to be deployable in modest amounts ofspectrum. The system and method described herein supports an entiremetro-area backhaul or BWA network with a single frequency channel, thusminimizing the need for large amounts of spectrum.

FIG. 6 illustrates an example of an implementation of both concentratingbackhaul radio 54 and the terminating backhaul radios 52 of the system.In particular, both the CBR 54 and each TBR 52 has four subsystemsincluding an antenna subsystem 100, a transceiver subsystem 102, abeamforming subsystem 104, such as a 2-dimensional beamforming systemand a baseband radio subsystem 106.

The antenna subsystem 100 may comprise a plurality of antennas 101, suchas N₁ as described above wherein N₁ is a predetermined number ofantennas in the adaptive array for each TBR or N₂ antennas wherein N₂ isa predetermined number of antennas in the adaptive array for the CBR.Each antenna has 2 feed points that are orthogonal (orquasi-orthogonal). For example, the orthogonal (or quasi-orthogonal)feed points may be vertical/horizontal,left-hand-circular/right-hand-circular, or slant left/slant right asexamples. The vertical/horizontal (V/H) feed points for each antenna areshown in FIG. 6 . Each antenna may be passive or active. The antennascan be arrayed in a linear array, a two dimensional array or a3-dimensional array. Example geometries of the antennas include flatpanel, circular, semi-circular, square or cubic implementations. Theantennas maybe placed in the array in an arbitrary fashion as well.

The transceiver subsystem 102 may further comprise a plurality oftransceivers 102 a, such as N₁ transceivers for each TBR and N₂ for theCBR, that provide one channel for each of the 2 polarization feeds fromthe associated antenna as shown in FIG. 6 . Each transceiver channelprovides a radio frequency (RF) receiver and an RF transmitter. Eachtransceiver 102 a provides coherent or quasi-coherent down-conversionand up-conversion between RF and a complex baseband.

Each RF receiver in each transceiver may include a preselection filter,a low noise amplifier, a mixer, low pass filter and local oscillator toconvert the RF signal down to the complex baseband in a well knownmanner. The complex baseband may be converted to digital in-phase andquadrature signals using two analog-to-digital converters in a converterunit 102 b.

Each RF transmitter in each transceiver may include twodigital-to-analog converters in the converter unit 102 b, two low passfilters, a mixer and a local oscillator (LO) to convert the basebandsignal to RF in a well known manner. For a TDD system, the LO can beshared between the receiver and the transmitter. The output of the mixerdrives an RF preamplifier, transmit (Tx) filter and power amplifiercompleting the transmitter. The transmitter and receiver are connectedto the antenna feed via a TR switch (TDD) or a diplexing filter (FDD).

The beamforming subsystem 104 may receive the signals from each of thetransceivers as shown in FIG. 6 . The beamforming subsystem may have aweigh processor 104 a and a beamforming network (BFN) 104 b that isimplemented using a processor to perform the beamforming processesdescribed below. In one implementation, a two dimensional (2D)space-time adaptive processing (STAP) or space-frequency adaptiveprocessing (SFAP) bidirectional beam forming network may be used. Thebeamforming subsystem 104 is also connected to the baseband radiosubsystem 106 that has a plurality of well known baseband radios (1 to Kin FIG. 6 ) that are coupled to a hub or switch to route the datatraffic.

FIG. 7 illustrates an example of a 2-dimensional beamforming networksubsystem 104. The subsystem is realized in the digital domain as atapped-delayline for each antenna polarization. The output of eachtapped delayline is summed with the outputs of the other delaylines foreach antenna and polarization to form the output. Two 2D-BFNs areimplemented, one for each polarization where the dimension of the2D-BFNs are 2N₁×K where K is the number of taps. Note that FIG. 7 showssignal flow a receiver described above. For the transmitter, the signalflow is reversed through the beamformer 104.

The computation of the weights for the 2D-BFN is mechanized by theweight control processor 104 c. The receiver signal vectors at the delaytaps are made available to the processor in order to compute the complexweights at each tap. A number of optimal and near optimal algorithms aredetailed in subsequent sections. The 2D-BFN may be implement in hardware(discrete logic, ASICs, SOCs), software (on a DSP, CPU or GPU), orfirmware (e.g. FPGA). Note the 2D-BFN may be implemented in the analogdomain at baseband, IF or RF.

At the CBR, two 2D-BFNs are implemented for each of the L TBRs attachedto the CBR. In this case, N₂ antennas are processed. The dimension ofthe 2D-BRNs is 2N₂×K where K is the number of taps. In a more efficientCBR implementation, a pair of 2D-BRN of dimension N_(2×)K may be used ifthe channel is reciprocal and the TBR uses a pair of 2N₂×K 2D-BRN.

The subsystem 104 may contain an optional data direction feedbackcircuit 104 d. This circuit and its advantages will be described laterin the description of the system.

Returning in FIG. 6 , the baseband subsystem 106 may further comprise adual channel baseband radio processer (BRP). The BRP is comprised of aphysical layer, media access controller (MAC) and a network layer. Thephysical (PHY) layer implements modulation/demodulation,coding/decoding, encryption/decryption, and other PHY functions. The MACprovides frame building, scheduling, queuing, flow control, and layer 2signaling. The network layer provides the interface between the corenetwork and MAC implementing encapsulation, packet inspection, shaping,policing, and QoS mechanism. The BRP can be implemented withindustry-wide radio standards such as GSM, W-CMDA, IEEE-802.16 and LTEor be implemented with a custom PHY and MAC.

Prorata Cost Advantage of the Point-to-Concentrating MultipointArchitecture

Traditional MW backhaul uses a point-to-point backhaul radioarchitecture. In the disclosed system, the point-to-concentratingmultipoint (P2CMP) architecture shares the cost of all common CBRequipment such as antennas, transceivers, LNAs, PAs, filters, localoscillators, system control, backplanes, powering, and cabling cost overL TBRs with capacity Q per link, thus lowering the overall cost of eachlink. Traditional point to multipoint (P2MP) cannot make the same claimsince the capacity per link is only Q/M. When P2MP is normalized to thecapacity of Q bps per link, the cost per link is often higher that theP2P equivalent, or the spectral efficiency is degraded by a factor of Lsuch that spectrum cost become prohibitive.

Simultaneous/Sequential Adaptive Array processing

The system described herein implements simultaneous array adaption ofall TBRs receiving the desired downlink CBR signals and sequentialadaption of each end of the link. Typically two independent data streamsare transmitted on the vertical and horizontal arrays from the CBR. AllTBRs compute receiver weight vectors {right arrow over (w)} of thedownlink that are applied to the TBR beamformers to estimate thedownlink signals. The TBRs also estimate the SINR, {right arrow over(γ)} for the data stream(s) and sends it to the other end of the link aspayload or signaling. The TBR transmit weights g are formed from thescaled conjugate of received weight vectors noting again the decorationdenotes uplink. The transmit weights are scaled by the power controlvariable and sent to the transmit beamformer where the uplink data isprocessed before sending the weighted data streams to the antennaarrays.

The CBR then receives all uplink signals from L TBRs and computesreceiver weight vectors w _(j) where j is the TBR link index. The uplinkSINR γ _(j) is also computed for each of the links and will be sent tothe TBRs on the downlink. Next, the transmit weights {right arrow over(g)}_(j) are computed from the scaled conjugate of the receive weights w_(j) and applied to the downlink data.

Note weight adaption ping-pongs in a sequential fashion between the CBRand TBR, improving the network's performance at each iteration as shownin FIG. 8 . Since the CBR computes j simultaneous weights in thepresence of the self interference of all TBRs, the method may be knownas simultaneous/sequential weight adaptation. This approach will lead toan optimal solution across the network provided the transmitter powersare also adaptively controlled according to a power control criteriadescribed earlier.

Channel Model

The channel model for the system and method can be decomposed into anarrowband representation where the received signal y_(i)(n) is a resultof receive beamforming using N₁ antennas and transmission beamformingusing N₂ antennas and propagation through an RF channel matrixconnecting transmit antennas to receiver antennas pair wise:y _(i)(n)=w _(i) ^(H) H _(ij) g _(j)√{square root over (p _(j))}d_(j)(n)+w _(i)ε_(i)(n)

where w_(i) is the N₁×1 weight vector at the end node for link i, H_(ij)is the N₁×N₂ complex channel matrix for the CBR associated with link jto the end node associated with link i, g_(j) is the N₂×1 normalizeddownlink weight vector, √{square root over (p_(j))} is the complextransmit voltage on the downlink j, d_(j)(n) is the transmit signal fordownlink j at time sample n and ε_(i)(n) is a complex white Gaussiannoise process seen at TBR i. The uplink and downlink RF channels aredepicted in FIG. 9 . The tilde decoration denotes uplink in FIG. 9 .From FIG. 9 , the following equation for the expected outputsignal-to-interference and noise ratio (SINR) seen be downlink i as,

$\begin{matrix}{\gamma_{i} \equiv {{{❘{w_{i}^{H}H_{ii}g_{i}}❘}^{2}{p_{i}/{\sum_{j \neq i}{{❘{w_{i}^{H}H_{ij}g_{j}}❘}^{2}p_{j}}}}} + {\sigma_{\varepsilon}^{2}w_{i}^{H}w_{i}}}} & \end{matrix}$ $\begin{matrix}{{{{{\gamma_{i} \equiv}❘{w_{i}^{H}H_{ii}g_{i}}}❘}^{2}{p_{i}/{\sum_{j \neq i}{{❘{w_{i}^{H}H_{ij}g_{j}}❘}^{2}p_{j}}}}} + {\sigma_{\varepsilon}^{2}w_{i}^{H}w_{i}}} & ({A1})\end{matrix}$ $\begin{matrix}{\gamma_{i} \equiv {{T_{ii}{p_{i}/{\sum_{j \neq i}{T_{ij}p_{j}}}}} + {\sigma_{\varepsilon}^{2}\gamma_{i}}} \equiv {{T_{ii}{p_{i}/{\sum_{j \neq i}{T_{ij}p_{j}}}}} + \sigma_{\varepsilon}^{2}}} & ({A2})\end{matrix}$ $\begin{matrix}{{T_{ij} \equiv {{\overset{\rightarrow}{w}}_{i}^{H}H_{ij}{\overset{\leftarrow}{w}}_{j}^{*}{p_{i}/{{\overset{\rightarrow}{w}}_{i}}^{2}}{{\overset{\leftarrow}{w}}_{j}}^{2}}}{T_{ij} \equiv {{{\overset{\rightarrow}{w}}_{i}}^{H}H_{ij}{\overset{\leftarrow}{w}}_{j}^{*}{p_{i}/{{\overset{\rightarrow}{w}}_{i}}^{2}}{{\overset{\leftarrow}{w}}_{j}}^{2}}}} & ({A3})\end{matrix}$ $\begin{matrix}{{g_{j} \equiv {{\overset{\leftarrow}{w}}_{j}^{*}/{{\overset{\leftarrow}{w}}_{j}}^{2}}}{g_{j} \equiv {{\overset{\leftarrow}{w}}_{j}^{*}/{{\overset{\leftarrow}{w}}_{j}}^{2}}}} & ({A4})\end{matrix}$ $\begin{matrix}{{p = \left\lbrack {p_{0},{p_{1}\ldots p_{N - 1}}} \right\rbrack^{T}}{p = \left\lbrack {p_{0},{p_{1}\ldots p_{N - 1}}} \right\rbrack^{T}}} & ({A5})\end{matrix}$ $\begin{matrix}{P = {{1^{T}{pP}} = {1^{T}p}}} & ({A6})\end{matrix}$

Optimal Power Control

If the channel between TBRs and CBRs is reciprocal or quasi-reciprocalwithin the time span of the adaptive loop, then it can be shown that theoptimal transmitter weights are the scaled conjugate of the receiverweights. This is known as retro-directive beamforming. Moreover, if thetransmit power is adaptively adjusted using an algorithm driven by thereceive SINR and a target SINR γ _(j), then the network of CBRs and TBRswill converge to their target SINRs using minimum total network power Pas described in the equations above. If the total network power can beminimized, then interference into adjacent cells is minimized thusenhancing the capacity of these cells and the overall networkperformance in general. The target SINR is determined by the bit errorrate requirements of the communication link as determined by themodulation and coding scheme.

One simple method of power control computes the new power level fromlast power level and ratio of the target SINR to the received SINR. Theequation can be expressed as:p(l+1)=p(l)*γ _(j)/γ_(j) p(l+1)=p(l)*γ _(j)/γ_(j)  (A7)

where γ _(j) is the target SINR to close the link at acceptable BER andγ is the SINR as defined above

In this embodiment, the system has equalization gains (to be definedlater) since the system needs the per-subcarrier equalization to bereflected in the power control on the transmit side of the equation. Theeffect is cumulative over all the nodes in the network. Note thisalgorithm estimates the SINR of link continuously. If it is too highwith respect to the target SINR, then the next Tx power is reduced byratio between the target and current SINR.

Each receiver will optimize its beamformer weights by maximizing theSINRs at both ends of the link. Normally we place no constraints on theweights. However it is possible to place structural constraints on theweights to simplify computations. If our optimization process increasesthe SINR and if our SINR targets remain constant; we will necessarilyobtain a new solution that decreases all of the transmit powers and thusreducing P according to the equation above.

NLOS, STAP, SFAP, Polarization, Multiuser Processing, Equalization &Subbanding

Non Line-of-Sight Propagation Model

For the system and method, the model of the received data x(n) can beexpressed as the sum of multipath signals arriving on p distinguishablepaths each with steering vector a_(p). The received data also includesspatial white Gaussian interference i(n) generated. Hence the model maybe expressed as:x(n)=Ad(n)+i(n)x(n)=Ad(n)+i(n)  (B1)A≡[a ₁ ,a ₂ , . . . a _(p) ]A≡[a ₁ ,a ₂ , . . . a _(p)]  (B2)d(n)≡[√{square root over (α₁)}e ^(−jθ) ¹ d(n−τ ₁),√{square root over(α₂)}e ^(−jθ) ₁ d(n−τ ₂) . . . √{square root over (α_(p))}e ^(−jθ) ₁d(n−τ _(p))]^(T)

where √{square root over (α_(p))}e^(−jθ) ^(p) √{square root over(α_(p))}e^(−jθ) ^(p) is the amplitude and phase of path p, a_(p) is thesteering vector for path p and τ_(p) is the time delay for path p. d(n)is the transmitted data and i(n) is the interference vector modeled asGaussian white noise. The dimension of matrix A is N antenna sensors byP multipaths.

The Space-Time Adaptive Processor

An estimate {circumflex over (d)}(n) of the original signal d(n) can berealized by processing the received data with a 2-dimensional filter inthe dimensions of space and time, hence a space-time adaptive processor(STAP). This filter may be written as the linear convolution of receivevector x(n) at time n with the K₁+K₂+1K₁+K₂+1 time taps of the filterwhere each time tap has coefficients w^(H)(k)w^(H)(k) for −K₁≤k≤K₂:w ^(H)(n)*x(n)≡{circumflex over (d)}(n)w ^(H)(n)*x(n)≡{circumflex over(d)}(n)  (C1)w ^(H)(n)*x(n)≡Σ_(K=−K) ₁ ^(K) ² w ^(H)(k)x(n−k)w ^(H)(n)*x(n)≡Σ_(K=−K) ₁ ^(K) ² w ^(H)(k)x(n−k)  (C2)w(n)≡[w _(H)(K ₁),w ^(H)(K ₁−1), . . . ,w ^(H)(−K ₂)]^(H)w(n)≡[w _(H)(K ₁),w ^(H)(K ₁−1), . . . ,w ^(H)(−K ₂)]^(H)  (C3)

The error between the output of the STAP filter {circumflex over (d)}(n)and the desired signal d(n) can be expressed as ε(n) ε(n). We seek tominimize the expected value of the error power μ μ. where we replace theexpectation with a time average over a suitably large interval over thetime index n.

$\begin{matrix}{{\varepsilon(n)} = {{{\hat{d}(n)} - {{d(n)}{\varepsilon(n)}}} = {{\hat{d}(n)} - {d(n)}}}} & ({C4})\end{matrix}$ $\begin{matrix}{\mu = {{\left\langle {❘{\varepsilon(n)}❘}^{2} \right\rangle_{n}\mu} = \left\langle {❘{\varepsilon(n)}❘}^{2} \right\rangle_{n}}} & ({C5})\end{matrix}$ $\begin{matrix}{{\varepsilon(n)} \equiv {{\sum\limits_{k = {- K_{1}}}^{K_{2}}{{w^{H}(k)}{x\left( {n - k} \right)}}} - {\hat{d}(n)}}} & ({C6})\end{matrix}$ $\begin{matrix}{{\varepsilon^{*}(n)} \equiv {{\sum\limits_{k^{\prime} = {- K_{1}}}^{K_{2}}{{x^{H}\left( {n - k^{\prime}} \right)}{w\left( k^{\prime} \right)}}} - {\hat{d}*(n)}}} & ({C7})\end{matrix}$

where the estimate of the signal and the signal conjugate is written asfollows:

$\begin{matrix}{{{\hat{d}}^{*}(n)} \equiv {\sum\limits_{k^{\prime} = {- K_{1}}}^{K_{2}}{{x^{H}\left( {n - k^{\prime}} \right)}{w\left( k^{\prime} \right)}}}} & ({C8})\end{matrix}$ $\begin{matrix}{{\hat{d}(n)} \equiv {\sum\limits_{k = {- K_{1}}}^{K_{2}}{{w^{H}(k)}{x\left( {n - k} \right)}}}} & ({C9})\end{matrix}$

The time averaged error power can be written as follows:

$\begin{matrix}{\mu = \begin{pmatrix}{{\sum\limits_{k = {- K_{1}}}^{K_{2}}{{w^{H}(k)}{x\left( {n - k} \right)}{\sum\limits_{k^{\prime} = {- K_{1}}}^{K_{2}}{{x^{H}\left( {n - k^{\prime}} \right)}w\left( k^{\prime} \right)}}}} -} \\{{{{\hat{d}}^{*}(n)}{\sum\limits_{k = {- K_{1}}}^{K_{2}}{{w^{H}(k)}x\left( {n - k} \right)}}} +} \\{{{\hat{d}}^{2}(n)} - {{\hat{d}(n)}{\sum\limits_{k^{\prime} = {- K_{1}}}^{K_{2}}{{x^{H}\left( {n - k^{\prime}} \right)}{w\left( k^{\prime} \right)}}}}}\end{pmatrix}_{n}} & ({C10})\end{matrix}$

Since the system would like to minimize the error power as a function ofthe tap weights to minimize the mean squared error, the partialdifferentials with respect to the tap weights can be taken as follows:

$\begin{matrix}{\begin{matrix}{\frac{\delta\mu}{\delta{w^{H}(j)}} = {\sum\limits_{k = {- K_{1}}}^{K_{2}}{{w^{H}(k)}{\sum\limits_{k^{\prime} = {- K_{1}}}^{K_{2}}{{x\left( {n - k} \right)}{x^{H}\left( {n - k^{\prime}} \right)}\left( {w\left( k^{\prime} \right)} \right.}}}}} \\{= {2{\sum\limits_{k^{\prime} = {- K_{1}}}^{K_{2}}{{R_{xx}\left( {{- k},k^{\prime}} \right)}{w\left( k^{\prime} \right)}}}}}\end{matrix}{{{{for}j} = k},{{{otherwise}0{for}j} = k},{{otherwise}0}}} & ({C11})\end{matrix}$ $\begin{matrix}{\begin{matrix}{\frac{\delta\mu}{\delta{w^{H}(j)}} = {{{\hat{d}}^{*}(n)}{\sum\limits_{k = {- K_{1}}}^{K_{2}}{{w^{H}(k)}{x\left( {n - k} \right)}}}}} \\{= {2{{\hat{d}}^{*}(n)}{\sum\limits_{k = {- K_{1}}}^{K_{2}}{x\left( {n - k} \right)}}}}\end{matrix}{{{{for}j} = k},{{{otherwise}0{for}j} = k},{{otherwise}0}}} & ({C12})\end{matrix}$ $\begin{matrix}{\frac{\delta\mu}{\delta{w^{H}(j)}} = {{{\hat{d}(n)}{\sum\limits_{k = {- K_{1}}}^{K_{2}}{{x^{H}\left( {n - k^{\prime}} \right)}{w\left( k^{\prime} \right)}}}} = 0}} & ({C13})\end{matrix}$ $\begin{matrix}{\frac{\delta\mu}{\delta{w^{H}(j)}} = {{{\hat{d}}^{2}(n)} = 0}} & ({C14})\end{matrix}$

Hence, the equations can be rewritten as follows:

$\begin{matrix}{\frac{\delta\mu}{\delta{w^{H}(j)}} = {{2{\sum\limits_{k^{\prime} = {- K_{1}}}^{K_{2}}{{R_{xx}\left( {k^{\prime},{- k}} \right)}{w\left( k^{\prime} \right)}}}} - {2{r_{xd}\left( {- k} \right)}}}} & ({C15})\end{matrix}$

where the following expressions are defined:r _(xd)(−k)≡

(n−k)d*(n)

_(n) r _(xd)(−k)≡

x(n−k)d*(n)

_(n)  (C16)R _(xx)(K′−k)≡R _(xx)(k′−k)≡

x(n−k)x ^(H)(n−k′)

_(n)R _(xx)(k′−k)≡R _(xx)(k′−k)≡

x(n−k)x ^(H)(n−k′)

_(n)  (C17)

Setting the partial derivatives to zero for each weight vector, theessential equations can be rewritten as:

$\begin{matrix}{{\sum\limits_{k^{\prime} = {- K_{1}}}^{K_{2}}{{R_{xx}\left( {k^{\prime},{- k}} \right)}{w\left( k^{\prime} \right)}}} = {r_{xd}\left( {- k} \right)}} & ({C18})\end{matrix}$

for −K₁≤k≤K₂−K₁≤k≤K₂. The above equation can be rewritten in matrix formas:R _(XX) W=R _(xd) R _(XX) W=R _(xd)  (C19)Where

$\begin{matrix}{{W \equiv \left\lbrack {{w^{H}\left( {- K_{1}} \right)},{w^{H}\left( {{- K_{1}} + 1} \right)},\cdots,{w^{H}\left( K_{2} \right)}} \right\rbrack^{H}}{W \equiv \left\lbrack {{w^{H}\left( {- K_{1}} \right)},{w^{H}\left( {{- K_{1}} + 1} \right)},\cdots,{w^{H}\left( K_{2} \right)}} \right\rbrack^{H}}} & ({C20})\end{matrix}$ $\begin{matrix}{{{R_{xd}(n)} \equiv \left\lbrack {{r_{xd}^{H}\left( K_{1} \right)},{r_{xd}^{H}\left( {K_{1} - 1} \right)},\cdots,{r_{xd}^{H}\left( {- K_{2}} \right)}} \right\rbrack^{H}}{{R_{xd}(n)} \equiv \left\lbrack {{r_{xd}^{H}\left( K_{1} \right)},{r_{xd}^{H}\left( {K_{1} - 1} \right)},\cdots,{r_{xd}^{H}\left( {- K_{2}} \right)}} \right\rbrack^{H}}} & ({C21})\end{matrix}$ $\begin{matrix}{{R_{xx} = \begin{bmatrix}{R_{xx}(0)} & \cdots & {R_{xx}\left( {{- K_{1}} - K_{2}} \right)} \\ \vdots & \ddots & \vdots \\{R_{xx}\left( {K_{1} + K_{2}} \right)} & \cdots & {R_{xx}(0)}\end{bmatrix}}{R_{xx} = \begin{bmatrix}{R_{xx}(0)} & \cdots & {R_{xx}\left( {{- K_{1}} - K_{2}} \right)} \\ \vdots & \ddots & \vdots \\{R_{xx}\left( {K_{1} + K_{2}} \right)} & \cdots & {R_{xx}(0)}\end{bmatrix}}} & ({C22})\end{matrix}$Rewriting in summation form

$\begin{matrix}{{\sum\limits_{k = {- K_{1}}}^{K_{2}}{{R_{xx}\left( {k^{\prime} + k} \right)}{W\left( k^{\prime} \right)}}} = {R_{xd}(k)}} & ({C23})\end{matrix}$

Fast Transform Methods for Solving the STAP Problem

The above equations are formulated as a correlation. Thus, a lineartransform via the well known Discrete Fourier Transform (DFT) to furthersimplify the computations are further simplified by replacing thecorrelation with multiplications in the transformed domain using a fastconvolution/correlation theorem efficiently implemented via the wellknow Discrete Fourier Transform (DFT). First, the DFT F is defined asthe K×K matrix transformation as follows:F≡[ω ^(mk) ]F≡[ω ^(mk)]  (D1)For 0≤m,k≤K−10≤m,k≤K−1 and ω=e^(−j2π/K)ω=e^(−j2π/K)

Note the property of the inverse DFT is as follows:F ⁻¹ =F ^(H) F ^(−i) =F ^(H)  (D2)

Given this definition, the correlation expression above in thetransformed domain can be rewritten as follows:

$\begin{matrix}{{F{\sum\limits_{k^{\prime} = {- K_{1}}}^{K_{2}}{{R_{xx}\left( {k,k^{\prime}} \right)}{W\left( k^{\prime} \right)}}}} = {{FR}_{xd}(k)}} & ({D3})\end{matrix}$ $\begin{matrix}{{\sum\limits_{k = 0}^{K - 1}{\sum\limits_{k^{\prime} = {- K_{1}}}^{K_{2}}{{R_{xx}\left( {k + k^{\prime}} \right)}{W\left( k^{\prime} \right)}\omega^{mk}}}} = {\sum\limits_{k = 0}^{K - 1}{{R_{xd}(k)}\omega^{mk}}}} & ({D4})\end{matrix}$For 0≤m,k≤K−10≤m,k≤K−1 and ω=e^(−j2π/K)ω=e^(−j2π/K) whereK≥K₁+K₂+1. K≥K₁+K₂°1. Let k+k′k+k′=q and k=q−k′k=q−k′

$\begin{matrix}{{\sum\limits_{q = 0}^{K - 1}{\sum\limits_{k^{\prime} = {- K_{1}}}^{K_{2}}{{R_{xx}(q)}\omega^{mq}{W\left( k^{\prime} \right)}\omega^{{mk}^{\prime}}}}} = {\sum\limits_{k = 0}^{K - 1}{{R_{xd}(k)}\omega^{mk}}}} & ({D5})\end{matrix}$ $\begin{matrix}{{\sum\limits_{q = 0}^{K - 1}{{R_{xx}(q)}\omega^{mq}{\sum\limits_{k^{\prime} = {- K_{1}}}^{K_{2}}{{W\left( k^{\prime} \right)}\omega^{- {mk}^{\prime}}}}}} = {\sum\limits_{k = 0}^{K - 1}{{R_{xd}(k)}\omega^{mk}}}} & ({D6})\end{matrix}$ $\begin{matrix}{{{{\overset{\_}{R}}_{xx}\left( {- m} \right)}{\overset{\_}{W}(m)}} = {{{{\overset{\_}{R}}_{xd}\left( {- m} \right)}{{\overset{\_}{R}}_{xx}\left( {- m} \right)}{\overset{\_}{W}(m)}} = {{\overset{\_}{R}}_{xd}\left( {- m} \right)}}} & ({D7})\end{matrix}$Where the over bar indicates the Discrete Fourier Transform as follows

$\begin{matrix}{{\overset{\_}{W}(m)} = {\sum\limits_{k^{\prime} = {- K_{1}}}^{K_{2}}{{W\left( k^{\prime} \right)}\omega^{- {mk}^{\prime}}}}} & ({D8})\end{matrix}$ $\begin{matrix}{{{\overset{\_}{R}}_{xd}\left( {- m} \right)} = {\sum\limits_{k = 0}^{K - 1}{{R_{xd}(k)}\omega^{mk}}}} & ({D9})\end{matrix}$ $\begin{matrix}{{{\overset{\_}{R}}_{xx}\left( {- m} \right)} = {\sum\limits_{q = 0}^{K - 1}{{R_{xx}(q)}\omega^{mq}}}} & ({D10})\end{matrix}$Finally, we can express the space-time filter solution asW(k′)=F ⁻¹ W (m)=F ⁻¹ R _(xx) ⁻¹(−m) R _(xd)(−m)W(k′)=F ⁻¹ W (m)=F ⁻¹ R _(xx) ⁻¹(−m) R _(xd)(−m)  (D11)For each of taps on the space-time filter −K₁≤k′≤K₂−K₁≤k′≤K₂.

Improving Computational Efficiency

Note that for efficiency, an FFT and IFFT can be used to replace the DFTin the above equations. In this case, replace 3K²3K² complexmultiply/accumulates to realize the matrix multiplications associatedwith the DFTs and IDFT with 3 log₂ K log₂ K complex multiply/accumulatesusing the fast Fourier transform method. This results in one to twoorders of magnitude savings depending on the length of the filter in thetime domain.

Furthermore, note that the weight solution for the space-time filterrequires the formation of K covariance matrices of dimension N×N and Kcross-correlation vectors of length N. This is a considerable reductionin computation complexity compared to the original problem.

Improving Numerical Accuracy

Now express R _(xx)(−m)R _(xx)(−m) in terms of its QR decomposition ofthe underlying data XR _(xx)(−m)= X ^(H) XR _(xx)(−m)= X ^(H) X   (D12)X=QR _(x) X=QR _(x)  (D13)

Where R _(x) R _(x) is the Cholesky factor of the covariance matrix R_(xx) R _(xx). The Cholesky factor is an upper triangular matrix andwhere QQ is a orthonormal matrixR _(xx)(−m,m′)= R _(x) ^(H) Q ^(H) QR _(x) R _(xx)(−mm)= R _(x) ^(H) Q^(H) QR _(x)   (D14)Q ^(H) Q=IQ ^(H) Q=I  (D15)

And finally, substituting the Cholesky factor for the covariance matrixleads to the following expression. Note that the equation may be solvedfor WW efficiently using two back substitutions.R _(x) ^(H)(−m,m′) R _(x)(−m,m′) W (m′)= R _(xd)(−m)R _(x) ^(H)(−m,m′) R _(x)(−m,m′) W (m′)= R _(xd)(−m)  (D16)

Space Frequency Adaptive Processing

The 2-dimensional STAP beamformer may be realized in the frequencydomain by exploiting the Fourier Transform of the baseband signals fromthe array. In this case, the signal is “channelized” by the transforminto multiple frequency subbands such that the array response isconstant or nearly constant across the subchannel. The implication isthat the subchannel frequency support should be a fraction of theinverse of the RMS delay dispersion of the signal's multi-pathcomponents. Hence, narrowband beamforming may be performed on eachsubchannel. This is known as Space Frequency Adaptive Processing (SFAP).

Note that the number of subchannels is approximately equal to the numberof STAP taps in the delayline. SFAP may be the preferred embodiment formany signal types including OFDM, OFDMA and SC-FDMA. These signals arenaturally constructed in the frequency domain using data subchannels,pilots for demodulation and preambles as can be observed by examiningthe specifications for LTE and 802.16. The formation the SFAP equationsbegin with a model of the beamforming symbols:Xw=d+e  (E1)

where X is the received signal matrix of M rows of time samples by Nantennas, w is the CBR receive beamforming weight vector of length K, dis the desired symbol vector of length M and e is the error in thismodel due to noise plus interference. Pre-multiply (D1) by X^(H) to get:X ^(H) Xw=X ^(H) d+X ^(H) eX ^(H) Xw=X ^(H) d+X ^(H) e  (E2)

The minimum mean squared error solution is obtained by choosing theweight vector so that the received signal matrix is orthogonal to theerror vector:X ^(H) eX ^(H) e=0  (E3)

Equation (E2) can be written as:R _(xx) w=R _(xd) R _(xx) w=R _(xd)  (E4)

where the auto-correlation matrix and the cross-correlation vector arerespectively:R _(xx) =X ^(H) XR _(xx) =X ^(H) X  (E5)R _(xd) =X ^(H) dR _(xd) =X ^(H) d  (E6)

Solving (E4) for the weight vector yields:w=R _(xx) ⁻¹ R _(xd) w=R _(xx) ⁻¹ R _(xd)  (E7)

Substituting (E7) into (E1) and solving for the error vector yields (E8)and the error power per symbol is as follows and expanding (E9) by (E8)yields (E10):e=X(X ^(H) X)⁻¹ X ^(H) d−de=X(X ^(H) X)⁻¹ X ^(H) d−d  (E8)σ_(e) ² =e ^(H) e/Nσ _(e) ² =e ^(H) e/N  (E9)Nσ _(e) ² d ^(H) d−d ^(H) X(X ^(H) X)⁻¹ X ^(H) dNσ _(e) ² d ^(H) d−d ^(H) X(X ^(H) X)⁻¹ X ^(H) d  (E10)

Comparing (E10) and (E7), the error power can be expressed as a functionof the weight vector:Nσ _(e) ² d ^(H) d−Re(R _(xd) ^(H) w)Nσ _(e) ² =d ^(H) d−Re(R _(xd) ^(H)w)  (E11)

The QR decomposition of X is:X=QR _(x) X=QR _(x)  (E11a)

where Q is an orthonormal matrix the same size as X (M rows ofsubcarriers by N antennas):Q ^(H) Q=IQ ^(H) Q=I  (E11b)

and R_(x)R_(x) the Cholesky factor matrix of the auto-correlation matrixand is a N by N upper-triangular matrix. Substituting (E11a) into (E5),we obtain:R _(xx) R _(x) ^(H) Q ^(H) QR _(x) R _(xx) =R _(x) ^(H) Q ^(H) QR_(x)  (E11c)

But because Q is orthonormal (D11b), the auto-correlation matrix issimply the product of two Cholesky factors:R _(xx) =R _(x) ^(H) R _(x) R _(xx) =R _(x) ^(H) R _(x)  (E12)

We then substitute the Cholesky factors of (E12) into the error power of(D10):Nσ _(e) ² d ^(H) d−R _(xd) ^(H)(R _(x) ^(H) R _(x))⁻¹ R _(xd)Nσ _(e) ² d ^(H) d−R _(xd) ^(H)(R _(x) ^(H) R _(x))⁻¹ R _(xd)  (E13)

which can be written as:Nσ _(e) ² =d ^(H) d−u ^(H) uNσ _(e) ² =d ^(H) d−u ^(H) u  (E14)

where the biased estimate of the desired symbol vector is:u=R _(x) ^(−H) R _(xd) u=R _(x) ^(−H) R _(xd)  (E15)

Note that u is the solution to the equation:R _(x) ^(H) u=R _(xd) R _(x) ^(H) u=R _(xd)  (E15a)

which can be solved by back substitution of the upper triangular matrixR_(x) ^(H)R_(x) ^(H) into R_(xd)R_(xd). Substituting (E12) into (A7)yields the weight vector:w=R _(x) ⁻¹ R _(x) ^(−H) R _(xd) w=R _(x) ⁻¹ R _(x) ^(−H) R_(xd)  (E15b)

which can also be written as:R _(x) w=R _(x) ^(−H) R _(xd) R _(x) w=R _(x) ^(−H) R _(xd)  (E15c)

By substituting (E15) into (E15c), we obtain:R _(x) w=uR _(x) w=u  (E15d)

which can be solved for ww by back substitution of the upper triangularmatrix R_(x)R_(x) into uu.

Equalization and Subbanding

The formulation of the (A1) through (A15) assumes that the matrix Xcontains M subcarriers in the estimation of the first and second orderstatistics. For each subcarrier, this may be satisfied by collecting Msubcarriers over the time interval of JT_(s) where T_(s) is the symboltime of the OFDM(A) baseband. J is selected to satisfy certainconstraints dictated by the mis-adjustment of the linear combiner withrespect to the desired signal. A nominal figure of merit for M is 4times the degrees of freedom (4×DOF) for a mis-adjustment loss of <1 dB.

Alternately, the time-bandwidth product constraint maybe satisfied byforming the first and second or statistics over M_(sc)×M_(sym)=Msubcarriers where M_(sym) is the number of subcarrier per subband andN_(sym) is the number of symbols required to satisfy the M subcarriertime-bandwidth product (TBP) constraint.

This formulation is valid provided that the phase and amplitude of thesteering vector is relatively constant over the subband of M_(sc)subcarriers. In fact, this method is advantageous in lowering the numberof training symbols to meet the TBR required for link adaption.

In the system, we note that while maximizing M_(sc) subcarriers subjectto the SINR constraints is advantageous, it ultimately fails as thereceived SINR declines as M_(sc) subcarriers gets too large subject tothe dispersion of the multipath. However, the method may add a finalprocessing step to improve performance for a constrained number ofsubcarriers and model the collection of data over the subband as aconstant steering vector perturbed by small variation in phase andamplitude. Often, this is a low order model in both amplitude and phase.Hence, is a small phase and amplitude ramp across the subband can beestimated accurately by pilot subcarriers present/insert in the basebandof the signal (e.g. Wimax and LTE).

So the final processing in the frequency domain is to collect the firstand second order statistics and to estimate the post beamforming phaseand amplitude tilt across the subband for receiver processing. Then upontransmit, conjugate the phase and apply the amplitude corrections whileapplying them to the transmitter weight derived from the receiver weightvector. Note that the phase and amplitude tilt is unique for eachsubcarrier within in the subband. Thus each subcarrier has a uniquelinear combiner Rx weight and Tx weight conjugate.

This process is defined as subband equalization and yield superiornetwork performance. It is an additional component in achieving EIC.

Equalization and Power Control

For SFAP, it may not be intuitively obvious how transmit equalizationhelps, there is still a relatively simple mathematical reason why itimproves performance. If the method looks at the sum total transmitpower on the uplink or on the downlink, reciprocity says that these twoquantities are equal and are used as a network wide performance metricwhich may be known as quantity P. On the downlink this as a function ofall the receiver weights at the TBRs called W, and as a function of allthe transmit weights at the concentrators G. Thus P(W,G) becomes thenetwork performance metric to be optimized. Technically this metric is afunction of the weights on each subcarrier. Optimizing the receiverweights at the TBRs yields, min_(W) P(W,G). Equalization, in thiscontext, optimizes components of W. At the TBRs, if the system does nottransmit with the conjugate of the equalization gains, then the methodis refusing to optimize over all the components of G. In terms of thedegrees of freedom associated with just the equalization components,that's half the degrees of freedom in the network and this performancesuffers. Better performance is achieved optimizing both transmit andreceive weights according to min_(W) min_(G) P(W,G).

Reciprocity proves that the optimal G are the conjugate of theconcentrator receiver weights and thus are included the equalizationgains as well. The effect is cumulative over all the nodes in thenetwork. The fact that P(W,G) is reciprocal means that optimizing overequalization gains and transmitting with them necessarily improves allnodes in the network.

In this system and method, it is more intuitive to think in terms ofwhat equalization does to the weights qualitatively. If a minimumcomplexity rank 1 beam is all that is required in the direction of theintended node, more degrees of freedom are then devoted to interferencecancellation. Thus equalization will improve the channel in thedirection of the intended node and that's all it has to do to improveoverall network performance.

Capacity Matching, MCS Downshifting

In this system and method, the real-time capacity requirements ofequipment attached (i.e. a base station) to and from the TBR can besensed and the modulation and coding scheme (MCS) can be adaptivelyadjusted to meet these requirement. This is known as MCS downshiftingand upshifting. In the downshifting scheme, a moving average of theuplink and downlink capacity is computed by subtracting the “filler”symbols from the total symbols in order to estimate the number of“traffic” symbols. Next, a new and lower MCS level is computed thatwould essentially pack all symbols and remove the filler. Headroom isadded to this computation so as not to remove all filler. This is nowthe safe MCS level and the downshift can be commanded to the new levelvia PHY signaling (e.g. MAP). In the upshifting scheme, the data queuesfor the uplink and downlink are monitored. If these are not emptied oneach transmission interval, a higher MCS is warranted and the safe MCSlevel can be computed from a queue statistics. The upshift can becommanded to the new level via PHY signaling (e.g. MAP). Since the SINRrequirements are lower for a MCS downshift, the TX power of the link canbe lowered reducing interference power. Thus, downshifting increases theoverall capacity of the network by allowing additional links (>L) orhigher MCS levels for other links.

Best Serving CBR, Network Resiliency and Handover

In this system and method, the TBRs may establish connections tomultiple CBRs for the purpose of selecting the best serving CBR. Thebest serving CBR may be sensed by computing the SINR of each link,estimating the quality of the multipath channel, determining the loadingof the CBR, estimating the potential SINR degradation to other linkscurrently connected to the CBR, or any combinations of these metrics.The TBR will then request connection to the best serving CBR andgenerate a neighbor list of other CBRs. The list will include therequired timing parameters and power levels to each CBR. Using theneighbor list, a TBR can quickly switch over to another CBR if eitherthe CBR fails or the propagation channel becomes impaired. This providesa level of network resiliency and reliability.

Subbanding and Subzoning

In this system and method, the full capacity Q bps of each link can besubdivided into L_(sb) sublinks with each with capacity Q/L_(sb). Thismaybe realized by using L_(sb) subbands in the frequency domain.Alternately, a frame of data symbols may be divided into L_(sb) subzonesin the time domain. Note, that various linear combinations of capacitymay be realized by aggregating integer numbers of subbands and/orsubzones. A combination of subbanding and subzoning is also supported.

Dual Polarization, Optimal Polarization Separation

For this system, the system may transmit with two independent datastreams d₁(n) and d₂(n)d₁(n) and d₂(n) on two different polarizationwith transmit weight g₁ and g₂g₁ and g₂ respectively. This effectivelydoubles the data rate. Unfortunately, there is cross-coupling betweenthe polarizations due to propagation through an RF channel that mixesthe polarization as shown in FIG. 10 .

The receiver sees a mixture of the desired data d₁(n)d₁(n) via theprinciple channel matrix H₁₁H₁₁ and an interference term d₂(n)d₂(n) viathe cross coupling matrix of the other polarization H₁₂H₁₂ according thefirst equation below. In a similar fashion, the receiver for theorthogonal polarization sees a mixture the desired data d₂(n)d₂(n) viathe principle channel matrix H₂₂H₂₂ and an interference term d₁(n)d₁(n)via the cross coupling term of the other polarization H₂₁H₂₁ accordingthe second equation below.x ₁(n)=H ₁₁ g ₁√{square root over (p ₁)}d ₁(n)+H ₁₂ g ₂√{square rootover (p ₂)}d ₂(n)+i ₂(n)x ₁(n)=H ₁₁ g ₁√{square root over (p ₁)}d ₁(n)+H ₁₂ g ₂√{square rootover (p ₂)}d ₂(n)+i ₂(n)  (F1a)x ₂(n)=H ₂₁ g ₁√{square root over (p ₁)}d ₁(n)+H ₂₂ g ₂√{square rootover (p ₂)}d ₂(n)+i ₂(n)x ₂(n)=H ₂₁ g ₁√{square root over (p ₁)}d ₁(n)+H ₂₂ g ₂√{square rootover (p ₂)}d ₂(n)+i ₂(n)  (F1b)

The first equation maybe recast as the desired signal being received onaperture a₁₁(n)a₁₁(n) in the presence of cross-coupled interference onaperture a₁₂(n)a₁₂(n) and generalized interference aperture i₁(n)i₁(n)where the apertures are defined here. The same is true for the secondequation.a ₁₁(n)=H ₁₁ g ₁ a ₁₁(n)=H ₁₁ g ₁  (F2a)a ₁₂(n)=H ₁₂ g ₂ a ₁₂(n)=H ₁₂ g ₂  (F2b)

Given this formulation, the optimal weights for the down link (CBR toTBR) can be computed by forming the 2N₁×1 receiver data vector andcomputing the relevant first and second order statistics below. This isthe optimal MMSE solution for narrowband signals.

$\begin{matrix}{{x(n)} = {{\begin{bmatrix}{x_{1}(n)} \\{x_{2}(n)}\end{bmatrix}{x(n)}} = \begin{bmatrix}{x_{1}(n)} \\{x_{2}(n)}\end{bmatrix}}} & ({F3a})\end{matrix}$ $\begin{matrix}{{\overset{\rightarrow}{w}}_{1} = {{R_{xx}^{- 1}R_{{xd}_{2}}{\overset{\rightarrow}{w}}_{1}} = {R_{xx}^{- 1}R_{{xd}_{1}}}}} & ({F4a})\end{matrix}$ $\begin{matrix}{{\overset{\rightarrow}{w}}_{2} = {{R_{xx}^{- 1}R_{{xd}_{2}}{\overset{\rightarrow}{w}}_{2}} = {R_{xx}^{- 1}R_{{xd}_{2}}}}} & ({F4b})\end{matrix}$

The equations above maybe extended in a straightforward fashion forwideband data receive in multipath using the STAP and SFAP solutionspreviously above.

For the uplink (TBR to CBR), the weight solutions can be computed asabove with 2N₂ degrees of freedom, or with substantially lowercomplexity via the equations below. In this case, this inventioncomputes weights using x₁(n)x₁(n) and x₂(n)x₂(n) instead of x(n)x(n). Wenote that the polarization wavefronts arrive without cross-couplingsince the TBR transmit weights were derived from the conjugate of thedownlink TBR receive weights which are known to removed thecross-coupling components.w ₁ =R _(x) ₁ _(x) ₁ ⁻¹ R _(x) ₁ _(d) _(i) w ₁ =R _(x) ₁ _(x) ₁ ⁻¹ R_(x) ₁ _(d) ₁   (F5a)w ₂ =R _(x) ₂ _(x) ₂ ⁻¹ R _(x) ₂ _(d) ₂ w ₂ =R _(x) ₂ _(x) ₂ ⁻¹ R _(x) ₂_(d) ₂   (F5b)

Note, any orthogonally polarized antennas sets may be substituted withthe same result such as vertical and horizontal, slant left and right,or RHCP and LHCP.

The Reference Symbols and Data Directed Feedback

The reference signals for link adaption may be realized from specialtraining symbols, embedded pilots (e.g OFDM pilots for datademodulation), preambles, statistical significant data replications,baseband signal replications (e.g. cyclic prefix) in either the time orfrequency domain, the signal's known constellation (known modulus), orby data directed feedback techniques using payload data or bycombinations of above.

In one embodiment of this system and method, it can be illustrated howthe reference signals may be utilized. In this scheme, the CBR sends thedesired vertical and horizontal reference signals d_(v)(k) and d_(h)(k)on the vertical and horizontal array respectively simultaneously. Thereference signals are generated by modulating OFMDA subcarriers in thefrequency domain using elements of codes derived from CAZAC sequences.Alternately, the reference signals can be the modulation on the datasymbols of a single carrier in the time domain. CAZAC codes are a set oforthogonal codes with constant amplitude and zero circularauto-correlation and low circular cross-correlation. Hence d_(v)(k) andd_(h)(k) have low or zero cross-correlation. The CAZAC codes can beexpressed as

${{d(k)} = {{e^{{- j}\; 2\pi{\frac{r}{L}\lbrack{{k^{2}/2} + {qk}}\rbrack}}\mspace{14mu}{for}\mspace{14mu} k} = 0}},1,{{\ldots\mspace{14mu} L} - {1\mspace{14mu}{and}}}$r  relatively  prime  to  L, q

CAZAC codes from the same family are assigned to each TBR within thefootprint of the CBR. Each TBR is assigned two CAZAC codes, one for eachpolarization. Because each code has low cross-correlation with theothers, high quality estimates of cross correlation vectors are formed.This is important to minimize array mis-adjustment of the linearcombiner due to noise weight vectors computed from the normal equations.w=R _(xx) ⁻¹ R _(xd) w=R _(xx) ⁻¹ R _(xd)  (F6)

For the SFAP embodiment, R_(xx) ⁻¹R_(xx) ⁻¹ and R_(xd)R_(xd) areestimated over a block of P*L/B subcarriers containing the referencesignals where P is the number of OFMDA symbols modulated by thereference signal and B is the number of subbands. A subband is definedas a group of K/B adjacent subcarriers where the relative differencesbetween steering vectors measured on each member subcarrier as small.Thus, the linear combiner weights for the receiver are updated for eachblock of reference signal subcarriers. The SINR of the received signalmaybe also estimated over this block. The SINR is useful fortransmission power control when relayed to the other end of the link.

Reference Symbols Derived from Data Directed Feedback

Often the 2D-BFN weight accuracy derived from above can be enhanced bycomputing the first and second order statistics over a longer timeinterval not limited to the reference symbols. In this case, the datapayload part of the frame may be used. One embodiment correlates adelayed copy of the received data at multiple tap delays with anestimate of the data re-modulated using the same modulation and codingscheme (MCS) of the link. The data covariance is computed over this sametime interval. This technique is known as STAP/SFAP data directedfeedback (DDF) from and is illustrated in the figure above.

By using DDF, the embodiment achieves higher efficiency and linkcapacity since fewer reference symbols are required for link convergencewhen supplemented with a payload-derived “reference symbols” extractedfrom the payload. Moreover, DDF may extract reference symbols from theentire receive interval. This enables robust interference cancellationof unmanaged interference occurring in the data payload part of thesubframe and but not available in the reference symbol part of thesubframe. In this case, this is the preference embodiment for unlicensedfrequency bands or licensed bands with unmanaged interference.

Multiuser STAP

In the system, the CBR performs a link “concentration” function bysimultaneously connecting to L TBRs using L (single polarization) or 2L(dual polarization) sets of STAP weights. The governing L equations aregiven below:

$\begin{matrix}{{\sum\limits_{k = {- K_{1}}}^{K_{2}}{{R_{xx}\left( {k^{\prime} + k} \right)}{W_{1}\left( k^{\prime} \right)}}} = R_{{xd}_{1}(k)}} & ({G1})\end{matrix}$

where the equation

-   -   is the index over L links connected to the CBR and    -   is the index over L links connected to the CBR and 1≤l≤L1≤l≤L.        Note for best performance, d_(l)d_(l) should have low or zero        cross-correlation among all d_(j)d_(j) where j≠lj≠l.

Multiuser SFAP

In the system, the CBR concentration function for L simultaneous linksto L TBRs may realized in the frequency domain yields the multiuser SFAPsolution. The governing L (or 2L for dual polarization) equations aregiven below:u _(l) =R _(x) ⁻¹ R _(xd) _(j) u _(l) =R _(x) ⁻¹ R _(xd) _(j)   (G2)R _(x) w _(l) =u _(l) R _(x) w _(l) =u _(l)  (G3)

where u₁

-   -   is the index over L links connected to the CBR and    -   in the index over L links connected to the CBR and 1≤l≤L1≤l≤L.        Note for best performance, d_(l)d_(l) should have low or zero        cross-correlation among all d_(j)d_(j) where j≠lj≠l.

Dynamic Multiuser Power Allocation

The CBR antenna power delivered by each power amplifier (PA) is the sumof all powers for L links as weighted by the complex element g_(m) ofthe transmit weight vector g where m is the antenna/PA index.

The power P of all links in given belowp=[p ₀ ,p ₁ . . . p _(L-1)]^(T) p=[p ₀ ,p ₁ . . . p _(L-1)]^(T)  (H1)P=1^(T) pP=1^(T) p  (H2)

Power must be allocated to each link to maintain the target SINR and thetotal power to each PA cannot exceed the P_(PA). One technique is toallocate equal maximum power P_(PA)/L for each link. This is a veryconservative method and suboptimal since some links require more powerand some require less due to distance variation from the CBR. Thismethod causes the power required at the PA to be over specified.

In the system, the power can be allocated differently according to thefollowing equations:p→p _(max) p→p _(max)  (H3)p _(pa) =Gp _(max) P _(pa) =Gp _(max)  (H4)f[p _(maxpa) ,p _(pa) ]→p _(max) f[p _(maxpa) ,p _(pa) ]→p _(max)  (H5)

where the columns of G contain the power in each element of the transmitweight vectors for the L links. In this implementation, p is the initialestimate of the link powers derived from initial ranging. The powerp_(pa) to each PA can then be evaluated using the power scaling factorsfrom each of L transmit weights contained in G post multiplied by theinitial estimate of p_(max). Based on the computed PA power, and avector of maximum permissible powers p_(max pa), a new p_(max) can becomputed by a variety of functions, methods and/or iterations. If thereis a reasonable spread between power requirements of the links due to“near-far” distance variation, then this method yields significantlybetter performance.

This system may thus be called dynamic multiuser power allocation andcan improve the power available to TBRs at the edge of coverage by 2-6dB depending on L, N₁, N₂ and spatial distribution of the end points.

While the foregoing has been with reference to a particular embodimentof the invention, it will be appreciated by those skilled in the artthat changes in this embodiment may be made without departing from theprinciples and spirit of the disclosure, the scope of which is definedby the appended claims.

The invention claimed is:
 1. A wireless communication system,comprising: a communication link having a first end and a second endthat communicate over reciprocal radio frequency channels, thecommunication link having at least two radios at each end of thecommunication link, each radio having a transmit beamformer bank and areceive beamformer bank; and at least one transmit beamformer bank ateach end of the communication link and at least one receive beamformerbank at each end of the communication link exchanging data with eachother to transmit data over the communication link; wherein eachbeamformer bank is a set of beamformers and each beamformer isconfigured to process a section of a frequency band of the communicationlink wherein each section is a subband of the frequency band and two ormore subbands span the frequency band, wherein at least one transmitbeamformer of the transmit beamformer bank is configured to use one ormore transmit beamforming weights to perform transmit beamforming,wherein at least one receive beamformer of the receive beamformer bankis configured to use one or more receive beamforming weights to performreceive beamforming, wherein at least one weight of the one or moretransmit beamforming weights and the one or more receive beamformingweights is a complex weight comprising a phase and an amplitude, the atleast one weight being specific to a subcarrier, and wherein the atleast one transmit beamforming weight is determined based on a scaledcomplex conjugate of a respective receive beamforming weight.
 2. Thesystem of claim 1, wherein the communication link has the first end andthe second end and wherein at least one transmit beamformer bank at thefirst end of the communication link generates a beam pattern and atleast one receive beamformer bank at the second end of the communicationlink receives the beam pattern to optimize the transmission of data overthe communication link.
 3. The system of claim 2, wherein the at leastone transmit beamformer bank at the second end of the communication linktransmits a beam pattern, based on the one or more receive beamformingweights, to the at least one receive beamformer bank at the first end ofthe communication link.
 4. The system of claim 3, wherein the at leastone transmit beamformer bank at the first end of the communication linkgenerates a beam pattern, based on the one or more receive beamformingweights, to the at least one receive beamformer bank at the second endof the communication link.
 5. The system of claim 4, wherein thetransmit and receive beamformer banks optimize the communication link inthe presence of same frequency interference from other sectors where twoor more concentrating nodes are co-located together where a sectorrepresents the radio coverage of a field of view.
 6. The system of claim4, wherein the transmit and receive beamformer banks optimize thecommunication link in the presence of same frequency interference fromother concentrating radio sites where two or more concentrating radiossites are in a same geographical area where they are close enough tocause intercell interference.
 7. The system of claim 4, wherein thetransmit and receive beamformer banks optimize the communication linkand in combination with a power control algorithm converges atheoretical optimal capacity while minimizing an overall transmit power.8. The system of claim 4 further comprising a power control processassociated with radios and wherein the transmit and receive beamformerbanks and the power control process maximizes a capacity of thecommunication link while using only local pilots/reference signalsavailable at the local receivers.
 9. The system of claim 1, wherein thecommunication link has a first end and a second end and wherein theradio at the first end of the communication link is a concentrating nodeand the radio at the second end of the communication link is an endnode.
 10. The system of claim 9, wherein the transmit beamformer bank ofthe concentration radio generates a downlink data signal and the receivebeamformer bank of the concentration radio receives an uplink datasignal.
 11. The system of claim 9 further comprising a plurality ofreceive beamforming banks and a plurality of transmit beamforming banksat each concentrating node and a plurality of receive beamforming banksand a plurality of transmit beamforming banks at each end node wherein aplurality of independent data streams are communicated across thecommunication link simultaneously for a termination node for a pluralityof subscribers associated with the end node, wherein each data stream istransmitted in the presence of other data streams at a same frequencywhere the interference from the other data streams is removed byinference cancellation.
 12. The system of claim 1, wherein the transmitand receive beamformer banks optimize the uplink communication linkdespite interference in the communication link.
 13. The system of claim1, wherein the transmit and receive beamformer banks optimize thedownlink communication link despite multipath in the communication link.14. The system of claim 1, wherein the transmit and receive beamformerbanks optimize the communication link using pilot signals and/orreference signals with or without data.
 15. The system of claim 1further comprising a plurality of receive beamforming banks at each endof the communication link and a plurality of transmit beamforming banksat each end of the communication link so that a plurality of independentdata streams are simultaneously communicated across the communicationlink, wherein each data stream is transmitted in the presence of otherdata streams at same frequency where an interference from the other datastreams is removed by inference cancellation.
 16. The system of claim 1where each end of the communication link's transmit and receivebeamformers, within the beamformer filter bank, self aligns transmit andreceive antenna patterns to optimize link performance per subband andsubzone.
 17. The system of claim 16, wherein a modulation and codingscheme (MCS) is adjusted via downshifting or upshifting to matchrequirements as determined by a signal to noise ratio and/or signal tointerference and noise ratio.
 18. The system of claim 1, wherein beamsand nulls of each subband may be directed and optimized for differentend nodes.
 19. The system of claim 1 where beams and nulls of eachsubzones may be directed and optimized for different end nodes.
 20. Thesystem of claim 1 where the beams and nulls of each combination ofsubband and subzone may be directed and optimized for different endnodes.
 21. The system of claim 1 where the beams and nulls of eachcombination of subband and subzone may be directed and optimized fordifferent end nodes by a scheduler in a media access controller (MAC).22. The claim of 20, wherein the beams and nulls of each combination ofsubband and subzone may be directed and optimized for different endnodes by the scheduler in the media access controller (MAC) according toend node Quality of Service (QoS).
 23. The claim of 1, wherein the beamsand nulls of each combination of subband and subzone may be directed andoptimized for different end nodes by the media access controller (MAC)according to QoS as adjusted by any downshifting required to meet QoS ina presence of other node interference.
 24. The system of claim 1 wherean end node is attached to client devices such as WiFi access points,Ethernet switches, routers, or other client devices implementingbackhaul for Ethernet drop applications.
 25. The system of claim 1,wherein the at least one transmit beamformer bank of a first radio ofthe at least two radios is configured to determine a first set oftransmit beamforming weights to optimize the communication link tobenefit a receiver in a second radio of the at least two radios.
 26. Thesystem of claim 25, wherein the at least one receive beamformer bank ofthe second radio is configured to determine a first set of receivebeamforming weights after the first set of transmit beamforming weightshave been determined, wherein the first set of receive beamformingweights is configured to optimize the communication link to benefit areceiver in the first radio.
 27. The system of claim 1, wherein thetransmit beamforming weights and the receive beamforming weights aredetermined sequentially based on alternating transmission and receipt ofdata between the at least two radios.
 28. The system of claim 1, whereina radio at the first end and a radio at the second end are configured toperform weight adaptation iteratively for the at least one weight of thetransmit beamforming weights and the receive beamforming weights. 29.The system of claim 28, wherein concentrator backhaul radios (CBRs) andterminating backhaul radios (TBRs) at each end of the communication linkare configured to sequentially perform the weight adaptation.
 30. Thesystem of claim 1, wherein the at least one transmit beamforming weightis further determined based on determining a phase tilt and an amplitudetilt of the respective receive beamforming weight, and wherein the phasetilt and the amplitude tilt is specific to each subcarrier in thesubband.
 31. A wireless communication system, comprising: acommunication link having a first end and a second end that communicateover reciprocal radio frequency channels, the communication link havingat least two radios at each end of the communication link, each radiohaving a transmit beamformer bank and a receive beamformer bank; and atleast one transmit beamformer bank at each end of the communication linkand at least one receive beamformer bank at each end of thecommunication link that exchange data with each other to transmit dataover the communication link; wherein each beamformer bank is a set ofbeamformers and each beamformer is configured to process a section of afrequency band of the communication link wherein each section is asubband of the frequency band and two or more subbands span thefrequency band, wherein at least one transmit beamformer of the transmitbeamformer bank is configured to use one or more receive beamformingweights to perform transmit beamforming, and wherein at least onereceive beamformer of the receive beamformer bank is configured to usethe one or more receive beamforming weights to perform receivebeamforming, wherein at least one of the one or more receive beamformingweights and at least one weight of the one or more transmit beamformingweights is a complex weight comprising a phase and an amplitude, andbeing specific to a subcarrier, and wherein the at least one of the oneor more transmit beamforming weights is based at least on a scaledcomplex conjugate of a respective receive beamforming weight.
 32. Thesystem of claim 31, wherein the radio at the first end of thecommunication link is a concentrating node and the radio at the secondend of the communication link is an end node and each beamformer bankgenerates M_(CN), M_(TN) spatial beams and spatial nulls where theM_(CN) is a number of antennas at the concentrating node and the M_(TN)is a number of antennas at the end node and a sum of spatial nulls andthe spatial beams is equal to M antennas where M is also called degreesof freedom (DOF) of an antenna array.
 33. The system of claim 32,wherein if M_(CN) is at least two and if M_(TN) is at least two and anumber of data streams is a least two, then by distributing the DOFsbetween the two ends of the communication link to provide furtheroptimization of a link performance in the presence of non-line of sightpropagation and co-channel interference.
 34. The system of claim 33 thathave a minimum interference cancellation capability bounded by the sumof M_(CN)−1 and M_(TN)−1.
 35. The system of claim 33 that has aninterference cancellation capability are bounded by the product ofM_(CN)−1 and M_(TN)−1.
 36. The system of claim 33, wherein each end ofthe communication link requires O(M³) arithmetic computations, whereindistributing the arithmetic computations among the concentrating nodeand end nodes results in network capacity optimality while distributingcomputation complexity among all nodes, results in significantrealizability.
 37. The system of 36, wherein DM-MIMO provides additionalcapacity and link speed gains relative to conventional Massive MIMOschemes.
 38. The system of claim 33, wherein the system achieves atheoretical maximum imbedded cellular capacity of a wireless networkgiven a target SINR and one or more DM-MIMO parameters.
 39. The systemof claim 33, wherein the transmit and receive beamformer banks optimizethe communication link using pilot signals and/or reference signals withor without data.
 40. The system of claim 32, wherein the transmit andreceive beamformer banks optimize the communication link in the presenceof same frequency interference from other sectors where two or moreconcentrating nodes are co-located together.
 41. The system of claim 32,wherein the transmit and receive beamformer banks optimize thecommunication link in the presence of same frequency interference fromother concentrating radio sites where two or more concentrating radiossites are in a same geographical area where they are close enough tocause intercell interference.
 42. The system of claim 32 furthercomprising a plurality of receive beamforming banks and a plurality oftransmit beamforming banks at each concentrating node and a plurality ofreceive beamforming banks and a plurality of transmit beamforming banksat each end node wherein a plurality of independent data streams arecommunicated across the communication link simultaneously for the endnodes for a plurality of subscribers associated with the end nodes,wherein each data stream is transmitted in the presence of other datastreams at a same frequency where an interference from the other datastreams is removed by inference cancellation.
 43. The system of claim31, wherein the transmit and receive beamformer banks optimize thecommunication link and in combination with a power control algorithmconverges a theoretical optimal capacity while minimizing an overalltransmit power.
 44. The system of claim 31 further comprising aplurality of receive beamforming banks at each end of the communicationlink and a plurality of transmit beamforming banks at each end of thecommunication link so that a plurality of independent data streams aresimultaneously communicated across the communication link, wherein eachdata stream is transmitted in the presence of other data streams at samefrequency where an interference from the other data streams is removedby inference cancellation.
 45. The system of claim 44, wherein thestreams are localized to an orthogonal polarization of vertical andhorizontal antenna elements, and wherein interference cancellationseparates two data streams from interference of other streams.
 46. Thesystem of claim 45, wherein the streams are allocated equally across allvertical and horizontal polarizations and wherein the interferencecancellation separates the two data streams from the interference of theother stream resulting in the optimal link rate and overall networkcapacity.
 47. The system of claim 31 further comprising a power controlprocess associated with radios and wherein the transmit and receivebeamformer banks and the power control process maximizes a capacity ofthe communication link while using local pilots/reference signalsavailable at the local receivers.
 48. The system of claim 31, wherein aradio at the first end and a radio at the second end are configured toperform weight adaptation iteratively for the at least one of the one ormore transmit beamforming weights and the at least one or more receivebeamforming weights.
 49. The system of claim 48, wherein concentratorbackhaul radios (CBRs) and terminating backhaul radios (TBRs) at eachend of the communication link are configured to sequentially perform theweight adaptation.
 50. The system of claim 31, wherein the at least oneof the one or more transmit beamforming weights is further determinedbased on determining a phase tilt and an amplitude tilt of therespective receive beamforming weight, and wherein the phase tilt andthe amplitude tilt is specific to each subcarrier in the subband.